Question

In the figure below, BD and AC are diameters of circle P.

What is the arc measure of DC in degrees?

Answer 1

`arc\ DC=30^o`

Explanation:

The picture of the question in the attached figure

The point P is the center of the circle (the drawing is not a scale )

step 1

Find the measure of angle ∠CPD

we know that

`m\angle CPD+150^o=180^o` ---> by supplementary angles (form a linear pair)

`m\angle CPD=180^o-150^o=30^o`

step 2

Find the measure of arc DC

we know that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it

so

`arc\ DC=m\angle CPD` ----> by central angle

therefore

`arc\ DC=30^o`